High School

What is the quotient of [tex]\frac{-8x^6}{4x^{-3}}[/tex]?

A. [tex]\frac{x^9}{32}[/tex]
B. [tex]4x^9[/tex]
C. [tex]-\frac{12}{x^2}[/tex]
D. [tex]-2x^9[/tex]

Answer :

To solve the expression [tex]\(\frac{-8 x^6}{4 x^{-3}}\)[/tex], follow these steps:

1. Simplify the coefficients:
[tex]\[
\frac{-8}{4} = -2
\][/tex]

2. Simplify the exponents:
When dividing like bases, subtract the exponents:
[tex]\[
\frac{x^6}{x^{-3}} = x^{6 - (-3)} = x^{6 + 3} = x^9
\][/tex]

3. Combine the simplified coefficient and exponent terms:
[tex]\[
\frac{-8 x^6}{4 x^{-3}} = -2 x^9
\][/tex]

So, the quotient of [tex]\(\frac{-8 x^6}{4 x^{-3}}\)[/tex] is [tex]\(-2 x^9\)[/tex].

Thus, the correct answer is:
[tex]\[
\boxed{-2 x^9}
\][/tex]

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